Ridge surface system for maintaining laminar flow

ABSTRACT

IN MANY APPLICATIONS WHERE FLUID FLOWS OVER A SOLID SURFACE, OR WHERE A BODY MOVES THROUGH A FLUID MEDIUM, LAMINAR, RATHER THAN TURBULENT OR SPERATED, FLOW IS DESIRABLE. FRICTION IN THE FLUID BOUNDARY LAYER IN COMBINATION WITH AN ADVERSE PRESSURE GRADIENT CAN CAUSE TURBULENCE OR SEPARATION EVEN ON A VERY SMOOTH SURFACE. AN ADVERSE PRESSURE GRADIENT EXISTS ON THE AFT PORTION OF MOST BODIES DUE TO THE DECELERATION OF FLUID WHICH HAS BEEN ACCELERATED OVER A CONVEX FORWARD PORTION. THE PRESENT INVENTION CREATES PATHS OF RELATIVELY FAVORABLE PRESSURE GRADIENT BY PROVIDING A SYSTEM OF SMOOTH RIDGES SHAPED AND LOCATED SUCH THAT THEY ACCELERATE CROSS FLOW COMPONENTS AS WELL AS THE FLOW IN THE FREE STREAM DIRECTION. THE RIDGES SWEEP SOME OF THE OUTER FLOW INTO THE BOUNDARY LAYER TO ENERGIZE THE LAYER IN AN ORDERLY FASHION. THE FLOW IN THE BOUNDARY LAYER IS ACCELERATED OVER THE RIDGES BECAUSE OF BOUNDARY LAYER THINNING AND BECAUSE THE RIDGES HAVE LESS CURVATURE THAN THE SURFACE. THEREFORE, THE RIDGES CAUSE LESS DECERLERATION OF THE FREE STREAM COMPONENTS THAN   THE SURFACE, CREATING PATHS FOR RELATIVE ACCELERATION OF FLOW UP THE RIDGES. IN ADDITION, THE RIDGES MAY BE SHAPED IN LATERAL CROSS SECTION TO CREATE A VENTURI BETWEEN TWO RIDGES. IF THE RIDGES ARE EXTENDED BEYOND THE TRAILING EDGE OF THE SURFACE RELATIVELY FAVORABLE PRESSURE GRADIENTS CAN BE MAINTAINED TO THE SURFACE TRAILING EDGE. THE RIDGE SYSTEM PERFORMS THE FUNCTION OF ENERGIZING THE BOUNDARY LAYER IN THE MANNER OF VORTEX GENERATORS WITHOUT INTRODUCING TURBULENCE. THE RIDGE SYSTEM ALSO PERFORMS THE FUNCTION OF A BOUNDARY LAYER BLEED SYSTEM WITHOUT MECHANICAL COMPLEXITY.

United States Patent [721 lnventor Scott C. Rethorst. Pasadena. Calif.{21] Appl. No. 790,35l

[22] Filed Jan. 10, i969 [45] Patented June 28. 197i {541 RIDGE SURFACESYSTEM FOR MAINTAINING LAMINAR FLOW 5 Claims. 10 Drawing Figs.

[52] L18. Cl 244/41 [51 Int. Cl 1364c 23/00 [50] Field of Search 244/41[56] References Cited UNITED STATES PATENTS Primary Examiner- MiltonBuchler Assistant Examiner- Carl A. Rutledge Attorney-Smyth, Rostan andPavitt ABSTRACT: ln many applications where fluid flows over a solidsurface. or where a body moves through a fluid medium. laminar. ratherthan turbulent or separated. flow is desirable. Friction in the fluidboundary layer in combination with an adverse pressure graident cancause turbulence or separation even on a very smooth surface. An adversepressure gradient exists on the aft portion of most bodies due to thedeceleration of fluid which has been accelerated over a convex forwardportion. The present invention creates paths of relatively favorablepressure gradient by providing a system of smooth ridges shaped andlocated such that they accelerate cross flow components as well as theflow in the free stream direction. The ridges sweep some of the outerflow into the boundary layer to energize the layer in an orderlyfashion. The flow in the boundary layer is accelerated over the ridgesbecause of boundary layer thinning and because the ridges have lesscurvature than the surface. Therefore, the ridges cause less declerationof the free stream components than the surface. creating paths forrelative acceleration of flow up the ridges. in addition, the ridges maybe shaped in lateral cross section to create a venturi between tworidges. If the ridges are extended beyond the trailing edge of thesurface relatively favorable pressure gradients can be maintained to thesurface trailing edge. The ridge system performs the function ofenergizing the boundary layer in the manner of vortex generators withoutintroducing turbulence. The ridge system also performs the function of aboundary layer-bleed system without mechanical complexity.

PATENTEUJUN28|97| I I 3588.005

SHEET 3 "OF 3 /NVENT'OR SCOTT C. RETHORST 1 BACKGROUND OF THE INVENTIONFlow of a fluid along a surface usually begins in laminar form. whichproduces little friction drag. Eventually. the laminar flow makes atransition to turbulent flow. which produces much higher friction drag.The causes ofthis break down in laminarity may include (1) surfaceroughness. (2) exterior energy sources. and (3) an adverse pressuregradient. The first two causes may be minimized by smooth fabricationand a nonturbulent environment. The third is more difficult to overcome.since any shape producing suction lift or enclosing a volume willgenerate a reduced pressure on its convex forebody (a favorable pressuregradient). and this pressure. in returning to free stream conditions aftof the body. must undergo an increase (an adverse pressure gradient)over some portion of the body. The flow is accelerated over the convexforebody. producing the favorable. negative pressure gradient anddecelerated over the aft portion of the body. producing the unfavorable.positive pressure gradient. This deceleration. combined with frictionalloss of energy in the boundary layer. decreases the ability of the flowto remain laminar. In the absence of a favorable pressure gradient or anoutside energy source. the laminar boundary layer will becomedisordered. i.e.. turbulent.

The region of adverse pressure gradient may be minimized by providing along forebody. i.e.. a long region of slight convex curvature such thatthe pressure gradient is small and favorable over much of the body. Theaft region of adverse pressure gradient is then shorter, although thegradient is more severe. This mechanism is the basis for theconventional laminar flow wing. The permissible severity ofthe aft.adverse pressure gradient. however. is limited by the necessity foravoiding flow separation. which produces very high drag.

Devices in current use to overcome the tendency for laminar to turbulentflow transition and/or for flow separation include vortex generators andsuction producing devices. Vortex generators operate by transferringenergy from the free stream into the frictionally decelerated(dc-energized) boundary layer. thereby providing energy to aid the flowin overcoming the adverse pressure gradient. This energy. however. isdisordered. i.e.. it tends to promote turbulence while delayingseparation. In addition. the vortex generators themselves create a dragenergy loss. though helping to avoid the greater separation energy loss.Suction devices may be installed in the body surface to provide afavorable pressure gradient on the aft portion of the body by sucking aportion of the boundary layer into the body. The flow must then beexhausted to the free stream by some mechanism. These suction devicesrequire power as well as extensive ducting and slotting of the bodysurface and therefore are quite complex.

The present invention. therefore. is designed to produce a region ofrelatively favorable pressure gradient on the portion of a body wherethe pressure gradient is normally adverse to aid in preventing laminarflow transition or separation. In addition. the invention will addordered rather than disordered energy to the boundary layer. thusavoiding the problems of vortex generators. and will be an integral partof the body surface. rather than a complex mechanism such as the suctiondevices.

BRIEF SUMMARY OF THE PRESENT INVENTION The present invention comprises aseries of ridges or waves integral with a solid surface and oriented atsome angle to or parallel to the free stream velocity vector. Theseridges are designed to fair smoothly into the surface but to projectabove it so that the surface curvature producing an adverse pressuregradient will be less on the ridges than on the normal surface. Thepressure gradient on the ridges may be adverse. relative to thefavorable pressure gradient on the fore portion of the surface. but willbe favorable relative to the adverse gradient on the aft portion of thenormal surface.

The flow over a surface tends to accelerate in the direction of afavorable pressure gradient and thus the ridges provide channels ofaccelerated flow in the free stream flow direction to add energy to theboundary layer and maintain flow laminarity in a region of normallyadverse pressure gradient. In addition. the ridges may be variable incross section with to provide a venturi effect to accelerate the flowbetween ridges and aid in maintaining laminar flow. The ridges mayproject beyond the aft end of the surface so that the adverse portion ofthe ridge pressure gradient will occur aft of the surface.

By providing regions of relatively favorable pressure gradient in thefree stream flow direction (or longitudinal direction) routes areprovided for any crosswise (or lateral) flow components to follow inorderly fashion. Normally, when the longitudinal flow in a boundarylayer is decelerated to such an extent that is can no longer negotiatean adverse pressure gradient, any crosswise flow componentsare-translated into random vortices which contribute to turbulence andseparation. In allowing a path for lateral acceleration of the flowthelongitudinal ridges utilize lateral flow energy to maintain ordered(laminar) longitudinal flow.

BRIEF DESCRIPTION OF THE DRAWINGS The foregoing and other readilyapparent features of my present invention will be better understood byreference to the following more detailed specification and accompanyingdrawings in which:

FIG. 1 is a cross sectional view of a general body of revolution showinga typical pressure distribution at zero angle of attack and at a zerolift condition.

FIG. 2 is a cross sectional view of a typical laminar flow wing showinga possible pressure distribution at an arbitrary. unstalled angle ofattack.

FIG. 3 is a schematic illustration of the velocity distribution in adecelerating boundary layer.

FIG. 4 illustrates a ridge system oriented normal to the free streamvelocity vector. wherein the ridges are of a height smaller than theboundary layer thickness.

FIG. 5 illustrates a ridge system oriented normal to the free streamvelocity vector. wherein the ridge height is greater than the boundarylayer thickness.

FIG. 6 is a three-dimensional view of a ridge oriented parallel to thefree stream velocity vector, illustrating flow acceleration up the sidesof the ridge.

FIG. 7 is a cross sectional view of a ridge on a typical wing,illustrating the ridge fairing and curvature relative to the normalsurface.

FIG. 8 is a three-dimensional view ofa ridge system applied to a body ofrevolution.

FIG. 9 is a three-dimensional view of a ridge system applied to theupper surface of a laminar flow wing.

FIG. 10 is a three-dimensional view of ridges having a minimum point ofdistance between them and projecting aft of the trailing edge of thenormal surface.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT In the followingparagraphs like numbers refer to the same or similar items from figureto figure.

In order to overcome the tendency of laminar flow over a surface toseparate or become turbulent the present invention utilizes a series ofridges in regions of adverse pressure gradient to create channelscfrelatively favorable pressure basic subsonic flow therory. if the crosssectional area available for a fluid to pass through is diminished. thevelocity must increase This increase in velocity reduces the pressureacting on the surface of the body creating areas of low pressure 22indicated on FIG. 1 by arrows pointing outward. The pressure continuesto decrease in the direction of flow 23 until the point of maximum bodythickness 24 is reached. This region 25 is an area of favorable pressuregradient and aids in maintaining laminar flow. Aft of the maximumthickness point the pressure begins a return to its original value.i.e.. that of the fluid at a large distance from the body. This region26 is an area of unfavorable pressure gradient and is detrimental toflow laminarity. Regions of positive pressure 27 (pressure greater thanatmospheric) exist at the nose of any body and may exist near the aftend if flow laminarity is not maintained.

The laminar flow wing cross section 28 shown in FIG. 2 is designed tohave the maximum thickness 24 fairly far aft so that the region ofdecreasing pressure 25 on the upper surface 29 will be more extensivethan if the maximum thickness were farther forward. The section shown inFIG. 2 is depicted as being pitched at an angle of attack 30 relative tothe free stream flow direction 23. This angle of attack could producethe positive pressure region 31 shown on the lower wing surface 32. Thesharp trailing edge 33 of the wing aids in preventing flow separationwhich could lead to positive pressures on the aft portion of the wing.but an adverse pressure gradient 26 still exists on the upper surfaceaft of the maximum thickness point.

Velocity distribution in the boundary layer of the fluid next to a bodysurface is commonly depicted as being in layers of increasing velocity34 as shown in FIG. 3. The velocity of the fluid in the layerimmediately next to the surface 29 is at zero velocity with succeedinglyhigher layers 34 increasing in velocity as the fluid molecules slip overthe layer below. until the upper region of the boundary layer 35 isreached. At this height 36. called the boundary layer thickness. thevelocity is approximately the same as the free stream velocity 23.Because of the friction caused by the fluid molecules slipping in layersnear the surface the velocity of the flow near the surface isprogressively decreased in the direction of flow. This is shown in FIG.3 as the arrows which indicate velocity of the layers 34 becomingshorter from left to right 37. When the velocity in several layers 38near the wall becomes zero the flow can no longer remain laminar. Eitherthe higher velocity upper layers will tend to curve down. creating smallvortices. random flow motion and. consequently. turbulence (creatinghigh friction drag). or the velocity near the wall will reverse 39.impelled by an adverse pressure gradient. and the flow will separatefrom the wall. creating large vortices 40 and high pressure drag.Therefore. in order to maintain laminar flow the energy lost in frictionmust be replaced by some mechanism.

One method of adding energy to the flow near the wall is to providesmooth ridges 41 such as are shown in FIG. 4. These ridges are withinthe boundary layer so that the boundary layer thickness 36 is decreased42 over the ridges 41. thereby accelerating the flow and maintaininglaminarity. In proceeding down the back side 43 of the ridge the flow 44tends to turn downward and some of the outer flow 23 is swept 45 intothe boundary layer 46. adding energy and maintaining laminar flow. Inaddition. the dead or very low velocity fluid 47 next to the bodysurface tends to be left on-the upwind side and the higher velocitylayers shear onto the ridge surface. creating a thinner. higher velocityboundeuy layer. By these mechanisms the ridges aid in maintaininglaminar flow in a direction normal to the ridges.

In the case of ridges 41 which project slightly above the boundarylayer; as shown in FIG. 5. fluid from the higher veloeitg.,23 regionoutside the boundary layer will be swept into the boundary layer 46 ofthe normal surface 29. This normal surface boundary layer thickness 36is less than the ridge height 48. The higher velocity fluid 45 willenergize the boundary layer. while creating accelerated flow 49 over theridges. helping to maintain laminar flow. As in the case of the ridgeheight 48 being less than the boundary layer thickness 36. thedecelerated flow next to the surface will be left in "dead areas 47 onthe upwind side of the ridges. Low velocity vortices will be formed inthese areas but should merely act to thicken the boundary layer on theupwind side 50 of a ridge. if the ridge is smoothly faired 51 into thenormal surface.

The height 48 of the ridges is limited by the adverse pressure gradienton the downwind side. If this pressure gradient is severe enoughseparation or turbulence 52 will occur on the downwind side. disturbingthe laminar flow. A favorable pressure gradient on the upwind side ofthe ridge and an unfavorable gradient on the downwind side are caused bythe same mechanism that creates gradients on the convex surfaces ofwings and bodies of revolution.

If the ridges 41 shown in FIGS. 4 and 5 are turned so that they runparallel to the direction of flow as shown in FIG. 6. the components offlow in the cross wise direction 53 will act in the same manner tomaintain flow laminarity as the free stream component 23 did when theridges were normal to the free stream flow. Such cross flow componentsusually exist on both wings and bodies of revolution. Both ends 54 and55 of the ridges are faired smoothly into the normal body surface 29 aswell as being faired on the sides 51.

Laminarity of the flow is usually thought of as being determined by theratio of inertia forces to viscous forces (known as Reynolds number).Above a certain value of this parameter (even for smooth surfaces) theflow will become turbulent or will separate. Reynolds number is commonlydefined only in the direction parallel to the free stream flow 23. Inaddition. most simplifications of the Navier-Stokes equations (the basicdescriptive fluid dynamics equations) neglect components which are notin the free stream direction. If ridges are introduced, however, thecross flow components 53 which normally exist on wings and bodies ofrevolution become important because of being accelerated by the ridges.Such acceleration of the cross or lateral flow components 53 takes placein both the lateral 53 and vertical 56 directions. For this reason,components of the flow which are commonly neglected may be utilized bysmooth ridges to become important in maintaining laminar flow.

Ridges 41 oriented in the free stream direction 23 also make use of thefree stream flow component 23 to maintain laminar flow. This mechanismis illustrated in FIGS. 6 and 7. At some point on a body surface 29moving through a fluid. the flow will normally become turbulent. Thispoint is represented by a dashed line 57. The ridge 41 is bugun 54upstream of this line 57 and is faired into the surface 29 so that itcontinues the body curvature 58 with. however. less curvature than thenormal surface 59. This difference in curvature results in the fluid 60on top of the ridge being decelerated less than the fluid 61 on the bodysurface as indicated in the figures by the ridge velocity arrow 60 beinglonger than the surface velocity arrow 61. Because of this velocitydifferential the pressure on the upper surface of the ridge will belower than that on the body surface. This pressure differential providesa path of flow 62 toward the ridge which is more favorable than the path63 into the adverse pressure gradient on the body surface. Thus, thefluid near the ridge is accelerated toward the upper surface 64 of theridge, adding energy to the boundary layer. This acceleration combineswith the cross flow component energy to maintain the laminar flow behindthe normal line of turbulence 57. The flow components 62 traveling upthe side of a ridge meet those accelerating up from the other side ofthe ridge-and both are swept along the top of the ridge in the freestream direction 23.

The difference in pressure distributions between the top of the ridge 64and the body surface 29 is shown in FIG. 7. The body surfacedistribution 65 is shown as a solid line while the ridge distribution 66is dashed. Behind the point of maximum thickness 24 the ridge pressure66 can be seen to drop off more slowly than the surface pressure 65 (Thepressures shown here are negative. as indicated by the outward arrows.and therefore a pressure "drop-off" is actually an increase. i.e.. it isunfavorable. Since the pressure gradient is the rate of change ofpressure with distance in the free stream direction 23 a greater rate ofpressure drop-off is unfavorable. At some distance down stream of thenormal body surface turbulence line 57 the adverse pressure gradientover the ridge will be great enough to cause turbulence. However. flowlaminarity will have been maintained over a larger portion of thesurface than without the ridges.

As in the case of the ridges normal to the free stream direction, theheight of the ridge will be determined by the necessity for avoidingflow separation 67. That is. the ridge must be fairedsmoothly 55 intothe aft edge 33 of thesurface 29 with a curvature less than that whichwill induce separatron.

A system of ridges could be utilized to maintain laminar flow on anybody enclosing volume which moves through a fluid. The ridges may beoriented at any angle to the principal flow direction 23 or parallel toit. FIG. 8 shows a ridge system installed on a generalized body ofrevolution 68. The flow sweeps aft 23. is accelerated up the sides ofthe ridges 62. and maintains laminarity to some region aft of the normalturbulence line 57. The cross flow components 53 are accelerated overthe ridges and may reduce the likelihood of separation near the aft end69 of the body by allowing the flow to *corkscrew" smoothly off the aftend rather than encounter the abrupt adverse pressure gradient in thefree stream direction caused by a blunted aft end.

A similar ridge system on a typical wing upper surface is shown in FIG.9. Inboard spanwise flow components 53 are produced on the uppersurfaces of finite wings because the pressure on the upper wing surface29 is lower than the free stream pressure. These components areaccelerated as th e y cross the ridges and the free stream directionflow 23 accelerates 62 up the sides of the ridges to maintain laminarflow aft of the normal surface line of turbulence 57. Again. the ridgesfair 54 into the surface 29 near the maximum thickness 24. on the edges51. and at the trailing edge 55. The abruptness of the aft fairing 55 isdetermined by the necessity for the avoidance of separation. A cutawayview 70 of the ridge structure is also shown in FIG. 9.

Another mechanism by which ridges could help maintain laminar flow overa surface 29 is illustrated in FIG. 10. In this case the flow isaccelerated between 71 the ridges 41 as well as over 62 the ridges.i.e.. a venturi effect is produced by shaping the ridges such that aminimum distance 72 between two ridges exists aft of the normalturbulence line 57. Thus. the flow between the ridges is accelerated upto the minimum distance point 72 because of the reduction in crosssectional area available for the flow in the boundary layer to passthrough. If the ends of the ridges 55 were extended aft from the normalaft edge 33 of the surface 29 the deceleration 73 created by thedistance between the ridges nqtsasi szwh sh rea ltsiy ea'ttt atalzlsnrsss trs gradient 26, would occur aft of the surface 29. By thismechanism a relatively favorable pressure gradient 25 could bemaintained over the entire surface. Thus, paths 71 for acceleration ofthe fluid would exist all the way to the aft end 33 of the normalsurface 29. Even if the trailing ends 55 of the ridges 41 extend only tothe trailing edge 33 of the normal surface 29, as shown in FIGS. 8 and9, lateral shaping of the ridges will create a region of relativelyfavorable pressure gradient aft of the normal turbulence line 57.

Other utilizations of ridge systems could be made in ducts. channels.pipes. nozzles. or on any structure over which flow laminarity isdesirable. The angle of the ridges to the flow would be determined bythe individual application. as would size and exact shape of the ridges.their orientation to each other. their location on the surface. and thenumber of ridges to be used.

The ridge system described in the preceding paragraphs provides uniquestructure to utilize the principles of fluid mechanics by providingchannels of relatively favorable pressure gradient in the region ofnormally unfavorable pressure gradient to maintain laminar flow in thisregion. By utilizing the flow in the higher velocity region of theboundary layer or in the stream external to the boundary layer toenergize and accelerate the lower flow in the boundary layer, the ridgesystem performs the function of vortex generators without generatingturbulence and performs the function of a suction system without themechanical complexity of such a system.

It is clear from this disclosure and its accompanying set of figuresthat the means of maintaining laminar flow have been described indetail. and the magnitude of the provisions disclosed may be variedaccording to engineering considerations for different conditions asrequired.

What is claimed is:

l. A streamlined body having a smooth surface. said body having amaximum thickness between its leading and trailing origins defining aforebody and afterbody. and a plurality of ridges protruding from saidsurface to a height of the order of the boundary layer thickness. saidridges beginning essentially at the point of maximum thickness andextending in the streamwise direction along the afterbody to essentiallythe end of said body, said ridges having a radius of curvature greaterthan that of the afterbody surface itself to provide favorable pressuregradient routes within the adverse pressure gradient field in theafterbody region to maintain laminarity in fluid flow past said body.

2. A streamlined body having a smooth surface and a plurality of ridgesprotruding from said surface to a height of the order of the boundarylayer thickness. said ridges extending in the streamwise direction andhaving a radius of curvature greater than that of the surface itself toprovide favorable pressure gradient routes to maintain laminarity influid flow past said body.

3. A streamlined body having a smooth surface and a plurality of ridgesprotruding from said surface. to a height of the order of the boundarylayer thickness. said ridges having a radius of curvature greater thanthat of the surface itself to extend into and impart higher energy flowinto the boundary layer to maintain laminarity in fluid flow past saidbody.

4. A smooth surface and a plurality of ridges protruding from saidsurface to a height of the order of the boundary layer thickness. saidridges extending in the streamwise direction to provide favorablepressure gradient routes to maintain laminarity in fluid flow past saidbody.

5. A smooth surface and a plurality of ridges protruding from saidsurface to a height of the order of the boundary layer thickness. saidridges providing locally accelerated flow to maintain laminarity influid flow over said surface.

